Question

before you continue, we recommend completing the day 2 activity.
\practice makes progress.\
which of the following best explains how the values of ( x ) and ( y ) can be calculated?
the value of ( x ) can be calculated using the equation ( 136 + x = 180 ), and the value of ( y ) can be calculated using the equation ( 22 + 136 = y ).
the value of ( x ) can be calculated using the equation ( 136 + x = 180 ), and the value of ( y ) can be calculated using the equation ( 22 + 136 + y = 180 ).
the value of ( x ) can be calculated using the equation ( 136 + x + 22 = 180 ), and the value of ( y ) can be calculated using the equation ( 22 + 136 + y = 180 ).

Explanation:

Step1: Find the value of \(x\)

Since \(x\) and \(136^{\circ}\) form a linear - pair (they are adjacent angles on a straight line), we use the equation \(x + 136=180\).

Step2: Find the value of \(y\)

The sum of the interior angles of a triangle is \(180^{\circ}\). In the given triangle, we know one angle is \(22^{\circ}\) and we can use the exterior - angle property (the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles). But also, using the angle - sum property of a triangle: \(22 + 136+y = 180\) (because the third angle of the triangle and \(136^{\circ}\) form a linear - pair, and we can re - express the angle - sum of the triangle in terms of the given angles).

Answer:

The value of \(x\) can be calculated using the equation \(136 + x=180\), and the value of \(y\) can be calculated using the equation \(22 + 136 + y = 180\).